Passage 2 Statistics
Correlations: Positive and Negative
A correlation is a mathematical tool that researchers can use to make a comparison between two different characteristics of a group. These characteristics are called variables, and correlations help describe the relationship between the two variables. There are many kinds of correlations: positive and negative, strong and weak, simple and complex. All of them provide important information to people who study specific attributes of populations.
Once a correlation is established, it can be quite helpful. Using a proven correlation, researchers only have to measure one of the two variables. Then they can predict the values for the second variable by applying a simple mathematical formula. This is far easier than having to measure both variables separately, for example, it has been proven that, on average, the more class sessions college students attend during a semester, the higher their final grade in that class will be. This correlation enables university professors or administrators to accurately predict a student’s GPA by looking at his or her class attendance record. Or, conversely, it allows them to estimate how well a class was attended by looking at the grades received by the students in that class.
==> This situation is an example of a positive correlation. As one variable increases, the other variable also grows by a proportionate amount In other words, the larger the number of classes students attend, the higher their grades will be. This relationship is easily plotted on a standard two-axis graph, with values on the horizontal x-axis representing one variable and values on the vertical y-axis representing the other. The x-axis values increase from left to right; the y-axis values increase from bottom to top. Because both sets of values in a positive correlation progress in the same way (increasing, in this case), a line will be graphed that slants up and to the right. This is the visual representation of a positive correlation.
==> Another well-known positive correlation exists between a person’s income level and his or her level of education. On average, the higher a person’s income, the more years of education that person has completed. Or, vice versa, the more years of education a person completes, the higher that person’s income will be. It is also possible to say that the lower a person’s education level, the lower his or her income will be. Any way you choose to describe it, the correlation is positive because both variables are moving in the same direction. They either increase together or decrease together, depending on your perspective.
=> In a negative correlation, however, the opposite occurs. As one variable increases, the other decreases by a proportionate amount Just as in a positive correlation, the direction that each variable moves individually is not important; it is the relationship between the movements of the two variables that matters. In a negative correlation, they progress in opposite directions. On a two-axis graph, the line symbolizing a negative correlation slants down and to the right. The downward movement represents the variable whose value decreases, and the rightward movement represents the variable whose value increases.
An established negative correlation exists between the number of hours of television a student watches per week and the grades that student receives in school. The more television the student watches, the lower his or her grades tend to be. Or, to say it another way, students who spend fewer hours watching television tend to have higher grades in school. Both of these statements describe the same negative correlation. Using this particular relationship, researchers can estimate how much television a child watches simply by observing his or her grade record.
==> Despite their practicality, correlations both positive and negative have one major disadvantage. They cannot determine or even predict whether the changes in one variable are actually caused by changes in the other. [A] For instance, researchers should not assume that watching television necessarily engenders bad grades.[B] The opposite might be true: students who frequently get bad grades become discouraged with schoolwork and choose to watch television instead. [C] This dilemma is part of the definition of correlations. [D] They can label a relationship as either positive or negative, but they cannot explain the causes behind the relationship.
14. The word attributes in the passage is closest in meaning to
15. The word it in the passage refers to
16. Which of the sentences below best expresses the essential information in the highlighted sentence in the passage? Incorrect choices change the meaning in important ways or leave out essential information.
(A) Research has shown that college students attend most of their classes every semester.
(B) The more class sessions a course has, the better attended it will be.
(C) Students that get high grades can be expected to attend most of their classes.
(D) Generally, students that attend more class sessions get higher grades.
17. According to paragraph 3, how does a two-axis graph display the variables of a correlation?
(A) Each axis corresponds to one variable.
(B) Each variable corresponds to one line on the graph.
(C) Each variable is represented on both axes.
(D) Each axis represents a positive correlation.
Paragraph 3 is marked with an arrow [==>].
18. According to paragraph 4, when one variable in a positive correlation increases, the other variable
(A) either increases or decreases depending on how you look at it
(B) stays approximately the same
(C) increases as well
(D) decreases by a proportionate amount
Paragraph 4 is marked with an arrow [==>]
19. In paragraph 5, how does the author explain the appearance of a negative correlation line on a graph?
(A) By comparing it to the graph of a positive correlation line
(B) By linking the line’s direction to the variables’ values
(C) By repeating the description of a two-axis graph
(D) By stating that the variables move in the same direction
Paragraph 5 is marked with an arrow [==>].
20. The word practicality in the passage is closest in meaning to
21. The word engenders in the passage is closest in meaning to
(B) comes after
(C) brings about
22. In paragraph 7, the author states that negative correlations
(A) offer more information than positive correlations
(B) are used less frequently than positive correlations
(C) do not work as well as positive correlations
(D) share a similarity with positive correlations
23. According to the passage, correlations do all of the following EXCEPT
(A) facilitate the study of two-variable relationships
(B) enable researchers to make predictions about relationships
(C) describe cause-and-effect relationships between variables
(D) create specific images on a two-axis graph
24. Look at the four squares H that indicate where the following sentence could be added to the passage.
Or there could be a third, unmeasured variable that acts on the relationship, such as the influence of the student’s parents.
Where would the sentence best fit?
25. Directions: Complete the table by matching the statements below.
Select the appropriate statements from the answer choices and match them to the type of correlation to which they relate. TWO of the answer choices will NOT be used. This question is worth 3 points.
Drag your answer choices to the spaces where they belong. To remove an answer choice, click on it To review the passage, dick View Text.
(A) Shows the relationship between the number of classes attended and a student’s final grade(B) Allows researchers to estimate a student’s grades by observing how much television the student watches(C) As one variable decreases, the other variable also decreases.(D) Shows the lack of any relationship between two variables(E) Can create a graphed line that progresses down and to the left
(F) As one variable decreases, the other variable increases.
(G) Predicts which variable is responsible for changes in the other variable